The density of humid air is calculated as follows:
\rho=\frac{p}{R_{\mathrm{wet}}\cdot\theta}
Here R_\mathrm{wet} is the specific gas constant for humid air:
R_{\mathrm{wet}}=\frac{R_{\mathrm{dry}}}{1-0,378\cdot\frac{p_\mathrm{v}}{p_\mathrm{a}}}
The factor in the denominator is calculated using the following relationship, where R_\mathrm{v} is the gas constant of water vapor:
0,378=\frac{\left(R_V-R_{dry}\right)}{R_V}
The water vapor partial pressure is calculated from the relative humidity and the saturation vapor pressure at dry bulb temperature:
p_{\mathrm{v}}=h_{\mathrm{rel}}\cdot p_{\mathrm{sat}(T_{\mathrm{dry}})}
For temperatures between 0°C and 100°C applies:
p_{\mathrm{sat}\left(T_{\mathrm{dry}}\right)}=610,8+44,442\cdot T_{dry}+1,4133\cdot T_{\mathrm{dry}}^2+0,0276\cdot T_{\mathrm{dry}}^3+2,55667\cdot 10^{-4} \cdot T_{\mathrm{dry}}^4+2,98166\cdot10^{-6}\cdot T_{\mathrm{dry}}^5